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BEGIN:VEVENT
UID:8fef5c429e1b772d54bfdc4b638aae3c
CATEGORIES:Geometry, Symmetry and Physics Seminar
CREATED:20220305T172255
SUMMARY:Integral Gromov-Witten invariants in genus zero
LOCATION:email organizers for zoom
DESCRIPTION:Gromov-Witten invariants of symplectic manifolds are roughly the counts of 
 pseudoholomorphic curves subjected to certain constraints. Because there ar
 e curves with nontrivial automorphisms, the invariants are essentially cert
 ain orbifold Euler characteristics. Hence the counts are in general rationa
 l numbers. In 1990s Fukaya and Ono proposed a method of defining an integer
  version of Gromov-Witten invariants using the (stable) almost complex stru
 cture on the moduli spaces. These integers can be viewed as the counts of p
 seudoholomorphic curves with trivial automorphism groups. Recently joint wi
 th Shaoyun Bai, we rigorously defined an integral Euler cycle of stable alm
 ost complex orbifold following Fukaya-Ono's proposal. As an application, us
 ing the recent construction of global Kuranishi charts on moduli spaces of 
 genus zero pseudoholomorphic curves by Abouzaid-McLean-Smith, we defined th
 e integer version of Gromov-Witten invariants in genus zero. This talk is b
 ased on the preprint  (https://arxiv.org/abs/2201.02688)https://arxiv.org/a
 bs/2201.02688\n
X-ALT-DESC;FMTTYPE=text/html:<p>Gromov-Witten invariants of symplectic manifolds are roughly the counts 
 of pseudoholomorphic curves subjected to certain constraints. Because there
  are curves with nontrivial automorphisms, the invariants are essentially c
 ertain orbifold Euler characteristics. Hence the counts are in general rati
 onal numbers. In 1990s Fukaya and Ono proposed a method of defining an inte
 ger version of Gromov-Witten invariants using the (stable) almost complex s
 tructure on the moduli spaces. These integers can be viewed as the counts o
 f pseudoholomorphic curves with trivial automorphism groups. Recently joint
  with Shaoyun Bai, we rigorously defined an integral Euler cycle of stable 
 almost complex orbifold following Fukaya-Ono's proposal. As an application,
  using the recent construction of global Kuranishi charts on moduli spaces 
 of genus zero pseudoholomorphic curves by Abouzaid-McLean-Smith, we defined
  the integer version of Gromov-Witten invariants in genus zero. This talk i
 s based on the preprint&nbsp;<a href="https://arxiv.org/abs/2201.02688" sty
 le="margin: 0px; padding: 0px; border: 0px; font-weight: 400; font-size: 15
 px; line-height: inherit; font-family: 'Segoe UI', 'Segoe UI Web (West Euro
 pean)', 'Segoe UI', -apple-system, 'system-ui', Roboto, 'Helvetica Neue', s
 ans-serif; vertical-align: baseline; letter-spacing: normal; orphans: 2; te
 xt-align: start; text-indent: 0px; text-transform: none; white-space: norma
 l; widows: 2; word-spacing: 0px; background-color: #ffffff;" data-auth="Not
 Applicable" data-linkindex="0"></a><a href="https://arxiv.org/abs/2201.0268
 8">https://arxiv.org/abs/2201.02688</a></p>
CONTACT:Guangbo Xu, Texas A&amp;M
DTSTAMP:20260930T190233
DTSTART;TZID=America/New_York:20220307T133000
DTEND;TZID=America/New_York:20220307T143000
SEQUENCE:0
TRANSP:OPAQUE
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